The biggest difference you're going to find is in memory addressing.
AWE is used by 32 bit Windows Operating systems. AWE is essentially a 2 step process, PAE is a 3 step process. So architecturally memory access is slower in 64 bit systems (Since Microsoft uses PAE as the memory management standard for X86_64 and AWE was the standard for 32 bit systems (you could enable PAE to get the extra gig of ram on an XP system, but this didn't make you 64 bit.)
64 Bit applications will be able to take advantage of the X86_64 instruction set, and 32 bit ones will require an "emulation layer" (that's not really what it does, but we'll pretend.) Further you will be able to address more of your memory for specific applications, and take advantage of 64 bit operations outside of WoW.
Wow utilizes DirectX like most other games out there. DirectX (unless built using the 64 bit SDK) has a limit on object sizes of 2gb, so there's no way you'll be getting any more memory use out of the system than you were before. And since 64 bit addressing is slower, it's not a performance gain there.
Honestly, if you want a performance boost the biggest bang for your buck would be a solid state disk that you have WoW loaded on. That and your GPU are the two system components that you're turning to slag. The memory component is really only an issue if you're constrained and paging to disk.
In terms of which to buy, I'd go with 64 bit since you're not really going to get a long life out of your 32 bit OS whatever it may be. Hardware vendors are going to eventually stop writing driver updates for your 32 bit OS and 64 bit is what the software companies are starting to focus on. Eventually It's likely there will be a World of Warcraft 64 bit client, but Blizzard will have to find a use case for storing more than 2gb in memory at any one point.